Maximum likelihood estimation in space time bilinear models

Dai, Yuqing; Billard, L.

doi:10.1111/1467-9892.00291

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…using the maximum log-likelihood estimation (MLE) method in [32,33]. MLEs draw conclusions from the observed data, particularly the joint probability distribution (see [34])…”

Section: Fixed Points and Stabilitymentioning

confidence: 99%

Study Models of COVID-19 in Discrete-Time and Fractional-Order

et al. 2023

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The novel coronavirus disease (SARS-CoV-2) has caused many infections and deaths throughout the world; the spread of the coronavirus pandemic is still ongoing and continues to affect healthcare systems and economies of countries worldwide. Mathematical models are used in many applications for infectious diseases, including forecasting outbreaks and designing containment strategies. In this paper, we study two types of SIR and SEIR models for the coronavirus. This study focuses on the discrete-time and fractional-order of these models; we study the stability of the fixed points and orbits using the Jacobian matrix and the eigenvalues and eigenvectors of each case; moreover, we estimate the parameters of the two systems in fractional order. We present a statistical study of the coronavirus model in two countries: Saudi Arabia, which has successfully recovered from the SARS-CoV-2 pandemic, and China, where the number of infections remains significantly high.

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“…using the maximum log-likelihood estimation (MLE) method in [32,33]. MLEs draw conclusions from the observed data, particularly the joint probability distribution (see [34])…”

Section: Fixed Points and Stabilitymentioning

confidence: 99%

Study Models of COVID-19 in Discrete-Time and Fractional-Order

et al. 2023

View full text Add to dashboard Cite

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“…This makes these bilinear processes part of discrete stochastic recurrence equations (Kesten, 1973;Le Page, 1983;Goldie, 1991), also known in Physics as linear discrete delay equations with multiplicative noise. Least-square estimators of the parameters of these bilinear models (Grahn, 1995;Bibi and Oyet, 2004) and conditional maximum likelihood estimation procedures (Dai and Billard, 2003) have been developed. …”

Section: (T) = A(t) E(t-1) + B(t) X(t) = H E(t-1) + G(t)mentioning

confidence: 99%

Properties of a simple bilinear stochastic model: Estimation and predictability

Sornette

Писаренко

2008

Physica D: Nonlinear Phenomena

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We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distribution from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others. IntroductionDaily asset returns in liquid markets exhibit two key statistical properties: (i) price changes are not auto-correlated beyond a few minutes, but (ii) the absolute values of changes are autocorrelated over long time scales leading to long-term persistence of the volatility. Hsieh (1995) noted that nonlinear processes can generate this type of behavior while linear process cannot. Volatility clustering, also called ARCH effect (Engle, 1982) is a clear manifestation of the existence of non-linear dependences between returns observed at different lags. (FI)-GARCH (Baillie et al

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“…Several generalizations of the original bilinear formulation have been proposed in the literature to re ect various time series features such as multivariate dependence (Stensholt and Tjøstheim [29]), change in regime (Ferrante, Fonseca and Vidoni [14], Aknouche and Rabehi [3]), spatial interaction (Dai and Billard [11]) and value discreetness (Doukhan, Latour and Oraichi [12]). A particular important extension dealing with periodic phenomena is the so-called periodic bilinear (PBL) formulation in which the parameters vary periodically over time.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of the first-order periodic autoregressive diagonal bilinear model

Aknouche¹,

Bentarzi²

2014

Random Operators and Stochastic Equations

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This paper studies stability problems and their consequences for the rst-order -periodic autoregressive diagonal bilinear (PBL(1, 0, 1, 1)) model in which the parameters vary periodically over time. Necessary and su cient conditions for strict periodic stationarity and periodic stationarity up to the th-order ( ≥ 1) of the PBL equation are provided. As a consequence, the autocovariance structure of the model is shown to have the periodic ARMA autocovariance structure and the kurtoses of the th-order periodically stationary solution are revealed. In addition, almost sure invertibility and mean-square invertibility of the PBL(1, 0, 1, 1) model are also considered. The paper gives a uni ed framework of stability that encompasses most of probability properties studied for the PBL model.

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Maximum likelihood estimation in space time bilinear models

Cited by 11 publications

References 17 publications

Study Models of COVID-19 in Discrete-Time and Fractional-Order

Study Models of COVID-19 in Discrete-Time and Fractional-Order

Properties of a simple bilinear stochastic model: Estimation and predictability

Stability analysis of the first-order periodic autoregressive diagonal bilinear model

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